The first time Paul Dano appears as Brian Wilson in “Love & Mercy,” it’s as if the movie is begging us to believe it. “It should be like a cry, but in a good way,” the actor mutters in soft falsetto, glancing at the floor and describing his sound. From there, director Bill Pohlad’s biopic ventures into the implications that tender statement, which cannily embodies the blend of celebration and melancholy at the root of the former Beach Boys singer’s music.

Co-written by Oren Moverman, whose unorthodox script for the Bob Dylan biopic “I’m Not There” covered decades of the singer’s life in non-traditional fashion, “Love & Mercy” similarly overcomes the boundaries of linear plot to cast Wilson’s struggles in a unique light. The narrative unfolds across two timelines at once: the sixties, in the aftermath of the Beach Boys’ first wave of fame, when an emotionally disturbed Wilson breaks away from the group to craft more adventurous sounds; and his more perilous state some two decades later, when he’s forced into the dictatorial care of therapist Eugene Landy (Paul Giamatti).

Portrayed during this part of the timeline by John Cusack, Wilson appears severely damaged and overmedicated. It’s in this near-vacant state that he encounters Cadillac salesperson Melinda Ledbetter (Elizabeth Banks), who attempts to date Wilson despite Landy’s insistence on monitoring the singer’s every move. While Landy insists that Wilson suffers from paranoid schizophrenic tendencies, Ledbetter launches a perilous battle to free the singer from his unorthodox incarceration — and, by extension, the demons of his past as we witness them pass by.

A delusional character himself, the domineering Landy could provide the focus of an entire movie in his own right, but Pohlad smartly keeps the story focused on Wilson’s talent and the way it confuses those around him. Coping with his abusive, wealthy producer father (slimily embodied by Bill Camp) and his concerned but routinely frustrated brothers, the sixties-era Wilson continually insists on breaking away from the one-note cheeriness of the group’s earlier albums. (“We’re not surfers,” he insists, “and real surfers don’t listen to us.”) Instead, Wilson presses for more inventive, sonically dense compositions that lead the group through several ups and downs, culminating with the blockbuster single “Good Vibrations.”

While Cusack’s scenes maintain a certain frantic sense of unease, the actor never fully breaks away from his familiar cadences. Dano, however, is a different story. His portrayal of Wilson as a jittery introvert, who gains several pounds as his mental condition rapidly worsens, marks the actor’s most accomplished performance to date.

Glancing furtively around the studio, he only comes to life when the music fits his needs. Pohlad layers the narrative with a complex audio design that makes it unclear whether we’re hearing actual music as it’s being performed or the haunting sounds inside Wilson’s head.

It’s fascinating to watch the songwriter dash frantically around the studio, orchestrating a dozen sounds into auditory unity that only he understands. No matter what else happens in the plot, “Love & Mercy” excels at placing the music front and center. Whether recording the same cello riff countless times over, or insisting on playing conflicting keys simultaneously, Wilson’s collage-like approach to sound turns into an abstract representation of his busy mental state.

By comparison, the scenes set in the later period don’t hold together quite as well, though the parallel narratives form a compelling contrast between Wilson’s unhindered artistic inclinations and the tragic outcome when he’s forced to suppress them. When his father rejects Wilson’s “God Only Knows,” deeming it “a suicide note,” he inadvertently nails the musician’s need to expunge his inner turmoil through orchestration.

That point is made too bluntly in the eighties-era scenes, which never satisfactorily merge with the past. Giamatti’s character turns Landy into a one-note villain (illustrating the challenge of casting an actor with the capacity to run wild with sleazy performances). Banks takes an admirable stab at playing Wilson’s determined savior, but her angelic qualities are so heavily foregrounded that she also strains credibility. Even so, Wilson makes for such an appealing oddball that it’s hard not to get swept up in the quest to save him, and that particular dynamic unfolds with an elegantly subdued quality that never forces the material to melodramatic extremes.

But before all else, “Love & Mercy” is an engrossing portrait of Wilson’s specific artistic inclinations, which draw from no real precedent. Cinematographer Robert Yeoman (best known for his credits on Wes Anderson films) conveys the lively Califonia setting in bright colors that strike a recurring contrast to Wilson’s troubled subjectivity. That same tension exists at the root of his artistry. In its best moments, “Love & Mercy” hovers in the same fragile space as the music.